Apparatus and methods for photonic integrated resonant accelerometer

ABSTRACT

The accelerometers disclosed herein provide excellent sensitivity, long-term stability, and low SWaP-C through a combination of photonic integrated circuit technology with standard micro-electromechanical systems (MEMS) technology. Examples of these accelerometers use optical transduction to improve the scale factor of traditional MEMS resonant accelerometers by accurately measuring the resonant frequencies of very small (e.g., about 1 μm) tethers attached to a large (e.g., about 1 mm) proof mass. Some examples use ring resonators to measure the tether frequencies and some other examples use linear resonators to measure the tether frequencies. Potential commercial applications span a wide range from seismic measurement systems to automotive stability controls to inertial guidance to any other application where chip-scale accelerometers are currently deployed.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to U.S. provisional application Ser.No. 62/168,276, filed May 29, 2015, entitled “PHOTONIC INTEGRATEDRESONANT ACCELEROMETER,” which is hereby incorporated herein byreference in its entirety.

GOVERNMENT SUPPORT

This invention was made with Government support under Contract No.FA8721-05-C-0002 awarded by the U.S. Air Force. The Government hascertain rights in the invention.

BACKGROUND

Accelerometers can find applications in many areas of technologies. Forexample, in the automotive industry, acceleration sensing is commonlyused for airbag deployment. The computer industry utilizesaccelerometers to protect hard disks from large shocks, and theaerospace industry employs inertial measurement units comprisingmultiple accelerometers and gyroscopes for sensing and navigation.Accelerometers are also used in many personal handheld devices as well,where they can detect the general orientation of the devices.

In many high volume applications, accelerometer devices are made usingmicroelectromechanical system (MEMS) fabrication technologies. Thesetechniques allow batch fabrication in a CMOS process flow and can havethe benefit of reductions in size, weight, power, and cost (SWaP-C)while maintaining adequate performance for a variety of applications.

Conventional MEMS accelerometers usually measure the electric charge ona capacitor to detect small movements of a proof mass attached to aspring so as to derive the acceleration of the proof mass. However, itcan be challenging for a conventional MEMS accelerator to detectacceleration on the order of sub milliG (1 G=9.8 m/s²) because thislevel of acceleration may only generate nanovolt changes that aredifficult to measure with high precision.

Optically-enabled accelerometers, where the capacitive pickoffs arereplaced with an optical transducer, can address the limits ofcapacitive accelerometers. Existing optical approaches typically rely onmeasuring small displacements of a mechanical proof mass and translatingthese displacements into acceleration. Therefore, the sensitivity of anoptical accelerator accelerometer depends on the precision of theoptical measurement system.

Displacement-based accelerometers can have resolutions down to 10⁻⁹ g,but they also suffer several limitations. First, any small displacementarising from thermal expansion, packaging stress, acceleration in anorthogonal dimension, or other unwanted drift can also be picked up bythe measurement system and erroneously translated into accelerationreadings. Second, some optically-enabled accelerometers exploitevanescent optical coupling to measure minute displacements, which canplace restrictions on the scale factor stability and full scale lineardynamic range of the device when operating in open-loop mode. Third,optical techniques that use highly sensitive interferometric measurementtypically also use optical sources with high levels of wavelengthstability and precision, creating a significant challenge to be appliedin small form factors and in harsh environments.

FIG. 1A shows a schematic of a displacement-based accelerometer 101including a proof mass 111 suspended by a pair of tethers 121 a and 121b from two anchors 141 a and 141 b. Each side of the proof mass 101 alsohas a respective measuring element 131 a and 131 b, connected to theanchors 141 a and 141 b, to measure the displacement of the proof mass101 with respect to the anchors 141 a and 141 b. The accelerometer 101is limited by the described above trade-off among sensitivity,stability, and dynamic range.

Resonant accelerometers (also referred to as frequency-modulatedaccelerometers) can relieve the constraints in displacement-basedaccelerometers by sensing acceleration based on detection of theresonant frequency of the tethers that suspend the proof mass.Acceleration of the proof mass causes opposing changes in the effectivestiffness of the tethers, resulting in equal but opposite shifts intheir resonant frequencies. Detection of this opposing shift can beutilized to calculate the acceleration of the proof mass, while anymutual shift of the tethers caused by unwanted orthogonal accelerationor temperature drift are cancelled out.

FIG. 1B shows a schematic of a resonant accelerometer 102 including aproof mass 112 suspended from two anchors 142 a and 142 b by two tethers122 a and 122 b, respectively. A pair of vibrating sensing tethers 132 aand 132 b, including electrostatic comb drives, are also attachedbetween the proof mass 112 and the anchors 142 a and 142 b.

In operation, the proof mass 102 experiences displacement as a result ofapplied acceleration. The displacement of the proof mass 102 pulls oneof the tethers (e.g., 132 a) into tension while pushing the other tether(e.g., 132 b) into compression, thereby altering the resonantfrequencies of the tethers 132 a and 132 b. The resonant frequencyshifts have equal magnitudes but opposite signs when the acceleration ofthe proof mass 102 occurs along the desired axis. Any acceleration, andresulting displacement, experienced in orthogonal dimensions can forcethe tether resonant frequencies to shift together, which allows for adifferential measurement and a cancellation of unwanted signals.

The two vibrating sensing tethers 132 a and 132 b can be excited anddetected using the electro-static comb drives. These comb drives can beused to both excite motion in the vibrating sensing tethers 132 a and132 b, typically at their natural mechanical resonant frequency, as wellas to detect this induced motion including measurement of the resonantfrequencies of the vibrating sensing tethers 132 a and 132 b.

The sensitivity of the resonant accelerometer 102 can be described bythe scale factor, or the amount of frequency shift experienced by anindividual sensing tether 132 a/132 b as a result of a givenacceleration of the proof mass 102 (e.g., in units of Hz/g). Generally,a larger scale factor is desirable, not only to increase systemsensitivity, but also to reduce the impact of unwanted drift in thesensor signal due to temperature and other fluctuations in thesurrounding environment over time. For example, in the case where thescale factor is equal to 10 Hz/g and the tether resonant frequency isstable to within 1 Hz over long periods of time, the measured signal, inunits of measured acceleration, usually drifts by 0.1 g over this time.If instead the scale factor is increased to 10 kHz/g and the tetherfrequency stability stays exactly the same, the measured signal maydrift by only 0.1 mg.

The scale factor depends on the ratio of the size of the proof mass 102to the size of the tethers 132 a/132 b, where larger proof masses andsmaller tethers can result in larger scale factors. The size of thesensing tethers 132 a/132 b is typically limited by the electro-staticcomb drives that both excite and detect their motion. Smaller tetherscan suffer from reduced detection sensitivity, which is dependent on thesurface area of the comb. This reduced sensitivity, combined withsmaller displacement amplitudes, can make it very difficult to monitormotions of tethers with cross-sectional dimensions of less than 10microns. This limits the achievable scale factor in conventional MEMSbased resonant accelerometers.

SUMMARY

For inertial navigation applications, the inventors have recognized adesire to improve the sensitivity of accelerometers while simultaneouslyimproving the drift stability of the measured signals over long timeperiods. Since acceleration measurements are integrated twice toretrieve position, any noise in the original signal can producesignificant errors in final assumed position. Consequently, there is alarge effort to improve the performance of these devices to reduce thismeasurement error. To date, accelerometers with improved performancetypically come at the expense of size and power, moving away from MEMSfabrication technologies to take advantage of a larger proof-mass inorder to achieve higher sensitivity and long term stability. Theinventors have recognized a desire to break this trade-off and developaccelerometers with excellent sensitivity and long-term stability whilemaintaining the low SWaP-C of MEMS devices.

Embodiments of the present technology address the desire to provideexcellent sensitivity, long-term stability, and low SWaP-C through acombination of photonic integrated circuit technology with standardmicro-electromechanical systems (MEMS) technology. Examples ofaccelerometers disclosed herein may have scale factors greater than 1kHz/g, which is an order of magnitude better than the current state ofthe art. In one example, an accelerometer includes a proof mass and atether, mechanically coupled to a side of the proof mass, to vibrate inresponse to acceleration of the proof mass. A ring resonator isevanescently coupled to the tether. Vibration of the tether causes achange of the resonance condition of the ring resonator. A detectionsystem is operably coupled to the ring resonator to sense the change ofthe resonance condition of the ring resonator.

In another example, a method of sensing acceleration with anaccelerometer comprising a proof mass, a tether mechanically coupled toa side of the proof mass, and a ring resonator evanescently coupled tothe tether is disclosed. The method includes detecting a change of aresonance condition of the first ring resonator caused by vibration ofthe tether in response to acceleration of the proof mass. The methodalso includes estimating the acceleration based at least in part on thechange of the resonance condition of the ring resonator.

In yet another example, a method of fabricating an accelerometerincludes fabricating a ring resonator in a first dielectric layerdisposed on a substrate. A second dielectric layer is deposited on thering resonator so as to fabricate a tether on the second dielectriclayer. A proof mass is defined and mechanically coupled to the tether byetching a back surface of the substrate. The method also includesetching the second dielectric layer below the tether so as to releasethe tether from the ring resonator.

In yet another example, an accelerometer includes a semiconductorsubstrate and a proof mass suspended from the semiconductor substrate bya first tether and a second tether. A first optical waveguide isoptically coupled to the first tether and a second optical waveguide isoptically coupled to the second tether. A first photodetector is inoptical communication with the first optical waveguide and a secondphotodetector is in optical communication with the second opticalwaveguide. In operation, the proof mass moves in a first direction inresponse to a force applied to the accelerometer. The first opticalwaveguide guides a first optical beam in a second direction orthogonalto the first direction such that motion of the proof mass causes achange in optical coupling between the first optical waveguide and thefirst tether. Similarly, the second optical waveguide guides a secondoptical beam in the second direction such that the motion of the proofmass causes a change in optical coupling between the second opticalwaveguide and the second tether. And the first and second photodetectorssense changes in the frequencies and/or amplitudes of the first andsecond optical beams caused by the change in optical couplings betweenthe optical waveguides and the tethers.

It should be appreciated that all combinations of the foregoing conceptsand additional concepts discussed in greater detail below (provided suchconcepts are not mutually inconsistent) are contemplated as being partof the inventive subject matter disclosed herein. In particular, allcombinations of claimed subject matter appearing at the end of thisdisclosure are contemplated as being part of the inventive subjectmatter disclosed herein. It should also be appreciated that terminologyexplicitly employed herein that also may appear in any disclosureincorporated by reference should be accorded a meaning most consistentwith the particular concepts disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The skilled artisan will understand that the drawings primarily are forillustrative purposes and are not intended to limit the scope of theinventive subject matter described herein. The drawings are notnecessarily to scale; in some instances, various aspects of theinventive subject matter disclosed herein may be shown exaggerated orenlarged in the drawings to facilitate an understanding of differentfeatures. In the drawings, like reference characters generally refer tolike features (e.g., functionally similar and/or structurally similarelements).

FIG. 1A shows a schematic of a displacement-based accelerometer.

FIG. 1B shows a schematic of a resonant accelerometer usingelectrostatic comb drives.

FIGS. 2A-2B show a perspective view and cross sectional view,respectively, of an optical circuit used to detect the tether frequencyin an accelerometer.

FIG. 3 is an example of transmitted power acquired by the accelerometershown in FIGS. 2A-2B to illustrate one mechanism of accelerationdetection.

FIGS. 4A-4B show a top view and perspective view, respectively, of aphotonic resonant accelerometer using a pair of ring resonators fordrift cancellation.

FIG. 4C shows a schematic of a balanced homodyne feedback circuit thatcan be used in the photonic resonant accelerometer shown in FIGS. 4A-4B.

FIG. 5 shows an example frequency spectrum detected by the accelerometer400 shown in FIGS. 4A-4B to illustrate one mechanism of accelerationdetection.

FIGS. 6A-6B show vibration frequencies of silicon and silicon nitridetethers, respectively, as a function of applied acceleration.

FIGS. 7A-7B show COMSOL simulations of a proof mass and tether systemhaving a smaller proof mass and long tethers.

FIGS. 8A-8B show COMSOL simulations of another proof mass and tethersystem having a larger proof mass and shorter tethers compared to thesystem shown in FIGS. 7A-7B.

FIG. 9 shows phase noise spectra of conventional opto-mechanicaloscillators (OMOs) and the OMO shown in FIG. 2A.

FIGS. 10A-10B are simulation results of frequency stability and biasstability of the OMO shown in FIG. 2A.

FIGS. 11A-11L illustrate a method of fabrication photonic integratedresonant accelerometers including ring resonators.

FIGS. 12A-12I illustrate a method of packaging photonic integratedresonant accelerometers.

FIGS. 13A-13B show schematics of photonic integrated resonantaccelerometers using linear resonators formed by distributed Braggreflectors.

FIGS. 14A-14B show schematics of photonic integrated resonantaccelerometers using silicon nitride evanescent sensing to detectacceleration.

FIG. 15 shows a schematic of a chip-scale photonic integrated resonantaccelerometer.

FIGS. 16A-16F illustrate a method of fabricating photonic integratedresonant accelerometers using linear resonators or tether-waveguideinteractions.

DETAILED DESCRIPTION

Overview

A Photonic Integrated Resonant Accelerometer (PIRA) can address thelimitations in conventional resonant accelerometer by replacing theelectrostatic comb drives with optically-sensed tethers. The motion ofthe tethers can be sensed through evanescent optical interactions usingintegrated waveguides, and acceleration can be calculated based onshifts in the tether resonance frequencies. For example, the tethers canbe evanescently coupled to a ring resonator. Small displacement of thetethers (e.g., induced by the finite temperature of the tether) canperturb the refractive index in the optical mode of the ring resonatorsuch that the resonance undergoes a slight shift. This shift results ina change in the transmitted optical power which can be measured on aphotodiode. The frequency at which the transmitted optical power changesgives an indication as to the vibration frequency of the tether, and anyshift in this vibration frequency can be used to estimate theacceleration.

In another example, the tether can include photonic materials such assilicon and function as one reflector, which is free to move with thetether, in a resonating structure (e.g., a Fabry-Perot resonator or adistributed Bragg reflector). The other reflector in the resonatingstructure can be fixed onto a silicon waveguide. The tether motion canchange the resonance condition of the resonating structure andaccordingly change the transmission power of light propagating in thesilicon waveguide. Therefore, the acceleration that causes the proofmass to move can be derived from the transmitted light power bymonitoring a shift in the oscillation frequency of the transmittedpower.

PIRAs can have several advantages over resonant accelerometers usingelectrostatic comb drives. First, the cross-sectional dimension of thetether can be dramatically reduced to, for example, on the order of 1 μmor less, which is approximately an order of magnitude smaller comparedto tethers currently used in state-of-the-art resonant accelerometers.Reduction of tether dimensions can lead to a large (>10×) improvement inscale factor. Second, the tethers in PIRAs can be made of electricallynon-conductive materials such as silicon dioxide or silicon nitride,which can be fabricated using existing mature semiconductor fabricationtechnologies. Silicon nitride can have excellent mechanicalcharacteristics under harsh environmental conditions. Sensitivityimprovements also allow for the use of a stiffer mechanical proof mass,which is more likely to withstand the required levels of shock andvibration.

In addition, interactions between optical and mechanical resonances canbe employed to produce opto-mechanical feedback effects, which can turnsimple mechanical resonators into self-sustained oscillators withimproved phase noise performance. The combination of higher scale factorand excellent frequency stability allows for the possibility to achievebias stabilities down to the 100 ng level and below. As understood inthe art, the bias of an accelerometer can be defined as the averageoutput over a specified time measured at specified operating conditionsthat have no correlation with input acceleration or rotation. Biasstability refers to the bounds within which the bias may vary over thespecified periods of time. Therefore, a lower value of the biasstability can mean that the accelerometer is less prone to noise inducedby, for example, environmental changes or other factors.

Furthermore, while the acceleration is measured by the optical circuits,the force-sensing mechanism is governed primarily by the mechanics ofthe device, including the tension or compression applied to the tethersby the proof mass. As a result, possible drift in optical wavelength orpower does not directly correlate to scale factor or bias drift in themeasurement. This can relax the performance requirements for theoptoelectronic components, which can be a significant advantage comparedto other optically-enabled accelerometer concepts.

PIRAs are also compatible with standard silicon photonics processing,where active components such as phase/amplitude modulators and photodetectors can be monolithically integrated alongside passive waveguides,splitters, and couplers. Heterogeneous bonding techniques can also beused to introduce optical sources on-chip as well. As a result, a trulychip-scale accelerometer can be constructed with all of the accompanyingoptoelectronic components integrated onto the same chip as the suspendedmicro-mechanical structure. The chip can also be vacuum packaged andeither wire or flip chip bonded to additional electronic circuitry forsignal processing.

PIRAs Using Ring Resonators

FIGS. 2A and 2B show the perspective view and the cross sectional view,respectively, of a PIRA 200 using ring resonators to sense acceleration.The accelerometer 200 includes a proof mass 210 (only a portion is shownin FIGS. 2A-2B) suspended over a substrate 260 by connecting to ananchor 250 via a tether 220. The proof mass 210 is free to move when anacceleration (or force) is applied to the proof mass 210 but the anchor250 is fixed. The motion of the proof mass 210 can stretch or squeezethe tether 220 depending on the direction of the acceleration, therebycausing the vibration frequency of the tether 220 to deviate from itscharacteristic vibration frequency when no stretching or squeezing isapplied on the tether 220.

A ring resonator 230 is evanescently coupled to the tether 220 such thatdisplacement of the tether 220 can alter the refractive indexexperienced by optical modes in the ring resonator 230. In other words,the displacement of the tether 220 can change the resonant condition(e.g., resonance wavelength) of the ring resonator 230. A detectionsystem 240 then detects the change of the resonance condition to monitorthe motion of the tether 220, including the vibration frequency, so asto further estimate the acceleration.

The proof mass 210 as shown in FIG. 2A has a rectangular shape forillustrating purposes only. In practice, the proof mass 210 can also besquare, round, elliptical, polygonal, or any other suitable shape. Itcan also be beneficial for the proof mass 210, in response toacceleration, to preferentially flex in the direction along the tether220 so as to more effectively stretch or compress the tether 220. Thematerial of the proof mass 210 can include, for example, silicon,silicon nitride, or any other material that is compatible with a MEMSfabrication processes such as complementary metal-oxide semiconductor(CMOS) fabrication processes.

The tether 220 in the accelerometer 200 translates the acceleration ofthe proof mass 210 into a change of its vibration frequency from thecharacteristic vibration frequency when no force is applied (alsoreferred to as the natural resonant frequency or simply naturalfrequency). The natural frequency of the tether 220 depends on, forexample, the material of the tether 220 and the dimensions of the tether220.

In one example, the detection system 240, as shown in FIGS. 2A-2B,includes a waveguide 242 evanescently coupled to the ring resonator 230and a detector 244 optically coupled to the waveguide 242. In operation,a light beam at a wavelength close to the resonant wavelength of thering resonator 230 can be transmitted through the waveguide 242. Atleast a portion of the light beam is coupled into the ring resonator 230due to the evanescent coupling between the waveguide 242 and the ringresonator 230. The transmitted power of the light beam is monitored bythe detector 244. When vibration of the tether 220, induced by theacceleration to be detected, perturbs the refractive index experiencedby the light beam, the transmitted power changes accordingly and can berecorded by the detector 244 to estimate the vibration frequency thetether 220.

In another example, the light beam transmitted through the waveguide 242and the ring resonator 230 can be a broadband light beam and thetransmitted spectrum of the light beam can be monitored by the detector244. Typically, spectral components at wavelengths close to the resonantwavelength of the ring resonator 230 are usually trapped within the ringresonator 230, thereby generating a valley in the transmitted spectrum.When motion of the tether 220 changes the resonant condition (includingthe resonant wavelength) of the ring resonator 230, the location of thevalley in the transmitted spectrum changes accordingly. Therefore, thevibration frequency of the tether 220 can be estimated by monitoring thetransmitted spectrum of the light beam.

Various materials can be employed to make the tether 220. In general, itcan be beneficial for the tether material not to absorb the light beam(e.g., at 1550 nm) propagating in the ring resonator 230 so as to reducethe chance of interference with the measurement of tether frequency. Inone example, the tether 220 can include silicon, silicon dioxide,silicon nitride, or any other material that is compatible with MEMSfabrication process (e.g., CMOS process). Silicon nitride also has largeinternal stress compared to other materials and therefore has lowmechanical damping, which can further lead to high quality (Q) factor ofthe tether vibration and higher sensitivity of the resultingaccelerometer. In another example, the tether 220 includes diamond,which has low internal mechanical damping and therefore can also providehigh Q factor for the tether 220. In yet another example, the tether 220can include aluminum nitride (AIN), which has low thermal expansion andtherefore is less prone to thermal noises. AIN can be fabrication by,for example, molecular beam epitaxy (MBE), reactive evaporation, pulsedlaser deposition (PLD), chemical vapor deposition (CVD), sputtering, andelectrophoretic deposition, among others.

The tether 220 can be defined by its width, height, and length. Thewidth of the tether 220 can be about 100 nm to about 2 μm (e.g., 100 nm,200 nm, 500 nm, 1 μm, 1.5 μm, or 2 μm). The height of the tether 220 canbe about 50 nm to about 500 nm (e.g., 50 nm, 100 nm, 200 nm, or 500 nm).The length of the tether 200 can be about 5 μm to about 200 μm (e.g., 5μm, 10 μm, 20 μm, 50 μm, 100 μm, 150 μm, or 200 μm).

In general, reducing the cross-sectional dimensions (e.g., height andwidth) of the tether 220 can result in higher sensitivity but may alsoreduce the linear dynamic range of the accelerometer 200, becausesmaller tethers tend to buckle or break under strong compression orstretching forces. This effect can be countered by, for example,reducing the length of the tether 220 or increasing the internal tensilestress of the material of the tether 220. Both approaches can increasethe natural frequency of the tether. Increasing the internal tensilestress can also reduce the damping of the mechanical resonance, therebyimproving the ultimate resolution.

Based on the materials and dimensions described above, the vibrationfrequency (also referred to as the resonance frequency) of the tether220 can be about 1 MHz to 1 GHz (e.g., 1 MHz, 10 MHz, 50 MHz, 100 MHz,200 MHz, 500 MHz, or 1 GHz). These vibration frequencies are at least anorder of magnitude higher than the resonant frequencies used in resonantaccelerometers based on electrostatic comb drives, which are limited notonly by the mechanical structure of the comb drives but also by therequisite transduction circuitry. Optical transduction techniquesalleviate these concerns, and can allow for tether resonance frequenciesbeyond 1 GHz, offering additional design flexibility when navigating theinherent trade-offs of dynamic range versus sensitivity.

The linewidths of the vibration frequency of the tether 220 can be about1 Hz to about 10 kHz (e.g., 1 Hz, 10 Hz, 50 Hz, 100 Hz, 500 Hz, 1 kHz, 2kHz, 5 kHz, or 10 kHz). In practice, there can be trade-offs in thechoice of tether frequency and linewidths. In general, higherfrequencies can result in a larger linear range, but can also make itharder to create narrow linewidths and accordingly higher sensitivity.On the other hand, lower frequencies are usually associated with smallerlinewidths and thus can yield good sensitivity. Therefore, it can bebeneficial to have large vibration frequencies but small linewidths(e.g., a linewidth less than 50 Hz, less than 20 Hz, less than 10 Hz,less than 2 Hz, less than 1 Hz, or less than 0.5 Hz).

The ring resonator 230 is evanescently coupled to the tether 220 tosense the motion of the tether 220. The strength of the evanescentcoupling can depend on the distance between the ring resonator 230 andthe tether 220. Generally, a smaller gap between the ring resonator 230and the tether 220 can result in a stronger interaction between thetether 220 and the light propagating in the ring resonator 230, therebyincreasing the sensitivity of the resulting accelerometer. On the otherhand, it is also desirable have a sufficiently large gap so as to allowthe tether 220 to freely move and vibrate in response to motion of theproof mass 210. In practice, the distance can be about 50 nm to about500 nm (e.g., 50 nm, 100 nm, 200 nm, 300 nm, or 500 nm). The gap betweenthe tether 220 and the ring resonator 230 can be filled with gas (e.g.,air) or vacuum.

The diameter (and accordingly the resonance wavelength) of the ringresonator 230 depends on, for example, the wavelength of the light beampropagating in the waveguide 242 and the ring resonator 230. Inpractice, the diameter of the ring resonator 230 can be about 5 μm toabout 200 μm (e.g., about 5 μm, 10 μm, 20 μm, 50 μm, 100 μm, 150 μm, or200 μm). The material of the ring resonator 230 can be, for example,silicon, silicon dioxide, silicon nitride, or any other material knownin the art.

Detection of Acceleration Based on Transmission Measurements

FIG. 3 illustrates one method for detecting acceleration using theaccelerometer 200 shown in FIGS. 2A-2B, where part of the waveguide inthe ring resonator 230 is disposed slightly below the tether 220. Whenthe tether 220 vibrates, the displacement dz is in the verticaldirection (z direction) and the distance (also referred to as the gapwidth) between the tether 220 and the ring resonator 230 changesperiodically depending on the vibration frequency of the tether 220.When the tether 220 is in its undisturbed position, the resonantwavelength of the ring oscillator 230 can be substantially equal to thewavelength of the light propagating in the waveguide 242 and thetransmitted power measured by the detector 244 is low. When the tether220 is away from its undisturbed position, the resonant wavelength ofthe ring resonator 230 changes accordingly and deviates from thewavelength of the light propagating in the waveguide 242. In this case,the transmitted power measured by the detector 244 can increase.Therefore, this periodic change in the gap width can induce theoscillation of the power transmission as shown in FIG. 3. Therefore, thevibration frequency of the tether 220 can be derived from theperiodicity of the oscillation of the power transmission. Once thevibration frequency and its deviation from the characteristic vibrationfrequency of the tether 220 are determined, the acceleration that causessuch deviation of vibration frequency can be determined accordingly.

PIRAs Including A Pair of Ring Resonators

FIGS. 4A and 4B show the top view and perspective view, respectively, ofan accelerometer 400 including a pair of ring resonators 430 a and 430 b(collectively referred to as ring resonators 430) on each side of aproof mass 410 to, for example, cancel out thermal drift in accelerationmeasurements. The proof mass 410 in the accelerometer 400 is suspendedfrom a pair of anchors 450 a and 450 b (collectively referred to asanchors 450) by two tethers 420 a and 420 b (collectively referred to astethers 420), each of which is attached to one side of the proof mass410. The anchors 450 are fixed on a substrate 460. Each tether 420 a/420b is also evanescently coupled to a respective ring resonator 430 a/430b, which can sense the motion of the tether 420 a/420 b via the changeof resonance conditions.

A light source 470 is disposed on the substrate 460 to provide a lightbeam for a detection system 440 to measure the vibration frequency ofthe tethers 420 and accordingly estimate the acceleration on the proofmass 410. The light source 470 can include any semiconductor laser. Theoperating wavelengths of the light source 470 can be, for example, about1310 nm, or about 1400 nm to about 1600 nm. Light at these wavelengthscan travel through silicon photonic circuits with negligible loss. Inaddition, the light source 470 can be fabricated separately and bondedto the substrate 460 after fabrication. The light beam is split into twoparts. The first part of the light beam is transmitted via a waveguide442 a, evanescently coupled to the ring resonators 430 a, to a detector444 a that monitors the transmitted beam power of the first part of thelight beam. Similarly, the second part of the light beam is transmittedvia a waveguide 442 b, evanescently coupled to the ring resonators 430b, to a detector 444 b that monitors the transmitted beam power of thesecond part of the light beam. The transmitted powers of the light beamacquired by the detectors 444 a and 444 b are transmitted to twofrequency detectors 446 a and 446 b, respectively, which can determinethe vibration frequencies of the two tethers 420. The frequencydetectors 446 a and 446 b can include commercially availablephase/frequency detectors, such as HMC 3716, HMC 984, and HMC 439manufactured by Analog Devices, or MC100EP140, MCH12140, and MCK12140manufactured by ON Semiconductors. A voltage-controlled oscillator (VCO)448 is coupled to the two frequency detectors 446 a and 446 b to providean input reference frequency (and/or phase) for the two frequencydetectors 446 a and 446 b.

A processing unit 449 then estimates the acceleration based on the twofrequencies detected by the two frequency detectors 446 a and 446 b. Themeasured frequency change can be a direct measurement of appliedacceleration, i.e., acceleration can be measured by simply measuring thetether frequency. More information about photonic circuits that canperform the measurements can be found in Galton, Ian, et al., Adelta-sigma PLL for 14-b, 50 kSample/s frequency-to-digital conversionof a 10 MHz FM signal, Solid-State Circuits, IEEE Journal of 33.12(1998): 2042-2053, which is hereby incorporated herein by reference inits entirety.

FIG. 4C shows a schematic of a balanced homodyne feedback circuit 500that can be used to maintain stable performances of the ring resonatorsover temperature. The circuit includes a sensing tether 520 connecting aproof mass 510 with an anchor 550. A ring resonator 530 is evanescentlycoupled to the tether 420. The ring resonator 530 also includes a phasetuner 535 to adjust (e.g., add or decrease) the phase delay of lightpropagating in the ring resonator 530. A laser 570 is employed as thelight source to provide light beam for acceleration detection. The lightbeam delivered by the laser 570 is transmitted through an input coupler542 a, which splits the light beam into two parts. The first part istransmitted to the ring resonator 530 via a waveguide evanescentlycoupled to the ring resonator 530. Possible residual light that is notcoupled into the ring resonator 530 is sent to a detector 545. The firstpart of the light beam propagating in the ring resonator 530 is coupledout by another waveguide and transmitted to an output coupler 542 b. Thesecond part of the light beam produced by the input coupler 542 a isdirectly sent to the output coupler 542 b, which combines the first partand second part of the light beam and deliver them into two detectors544 a and 544 b. The circuit 400 also includes a loop filter 580 tomaintain the phase matching between the oscillator 585 for the twodetectors 544 a and 544 b and the input phase into the ring resonator530.

FIG. 5 illustrates a frequency spectrum detected by the two frequencydetectors 446 a and 446 b to illustrate a method of sensing accelerationusing the accelerometer 400 shown in FIGS. 4A-4B. The spectrum includesa natural frequency of the tethers f₀ (the two tethers 420 have the samenatural frequency in this case). Under the acceleration and/or otherforces such as thermal expansion, the first tether 420 a has a firstdetected frequency f_(a) and the second tether 420 b has a seconddetected frequency f_(b). Any acceleration experienced by the proof mass410 in the desired dimension act equally on both tethers 420 a and 420 bbut with opposite force, in which case f_(a) and f_(b) are on differentsides of the natural frequency f₀. In contrast, any mutual shift in thetether frequencies (e.g., f_(a) and f_(b) on the same side of thenatural frequency f₀) can be attributed to either temperaturefluctuations or displacement of the proof mass 410 in an orthogonaldimension.

Characterization and Analysis of PIRAs Using Ring Resonators

Proof Mass and Tether Mechanical System

The performance of a resonant accelerometer can be described by themechanics of the proof mass and tether system. The vibration frequency(f) of the tether, as a function of the applied acceleration (a), can beexpressed as:

$\begin{matrix}{f = {\frac{i^{2}\pi}{2\; l^{2}}\sqrt{\frac{EI}{\rho \; {wh}}}\sqrt{{1 \pm {\frac{M_{p}l^{2}}{i^{2}{EI}\; \pi^{2}}a}} + \frac{{Sl}^{2}}{i^{2}{EI}\; \pi^{2}}}}} & (1)\end{matrix}$

where l, w, h are the length, width, and height of the tether, I is themoment of inertia for the vibrational mode, E and ρ are the Young'smodulus and density of the tether material, i is an integer mode index,and M_(p) is the mass of the proof mass. S is an extra force component.For example, tethers made of silicon nitride can have additionalinternal tensile stress that is accumulated during material deposition.

FIGS. 6A-6B show vibration frequencies of silicon and silicon nitridetethers, respectively, as a function of applied acceleration. The scalefactor of an accelerometer, also referred to as the frequency change asa function of applied acceleration (in units of Hz/g), can be estimatedby the slope of the curves shown in FIGS. 6A-6B. The minimum sensitivityof the accelerometer can be determined by the ratio of the scale factor(how much the frequency shifts as a function of acceleration) to thefrequency stability of the tether resonance.

FIG. 6A shows the vibration frequencies of a tether made of singlecrystalline silicon without internal stress (S=0). This silicon materialis similar to that used in state-of-the-art MEMS resonant accelerometersbased on electrostatic comb drives. But the cross-sectional dimensionsof the tether in FIG. 6A is less than 1 μm, about an order to magnitudesmaller compared to tethers in conventional resonant accelerometers. Thetether also has a height if about 200 nm and a length of about 250 μm.The mass of the proof mass is about 5×10⁻⁹ kg. The scale factor for thisdevice is about 4 kHz/g. For comparison, state-of-the-art MEMS resonantaccelerometers typically have cross-sectional dimensions larger than 10μm and scale factors in the range of about 0.1-0.2 kHz/g.

On the one hand, shrinking the size of the tether can increase thesensitivity by over an order of magnitude as seen in FIG. 6A. On theother hand, however, smaller dimensions of the tether may also cause thebehavior of the tether to be non-linear and limit the dynamic range ofthe resulting accelerometer. Smaller sizes may also cause the tether tobuckle under strong compression with only (e.g., ˜6 g of inertial forceaccording to Equation (1) when the value under the second square rootbecomes negative). This issue can be addressed by using materials withhigh tensile stress (e.g., silicon nitride) and/or increasing the sizeof the proof mass.

FIG. 6B shows a plot of vibration frequencies of a silicon nitridetether with the same geometric dimensions as the silicon tether shown inFIG. 6A but with an internal tensile stress approaching 1 GPa. Thislevel of tensile stress can be obtained by depositing stoichiometricsilicon nitride using low pressure chemical vapor deposition (LPCVD). Byaltering these mechanical characteristics (e.g., tensile stress), thehigh scale factor is maintained while the linearity and dynamic rangeare improved dramatically. The analytical expression in Equation (1) candescribe the mechanical resonance frequency of the tether and can beused to understand the basic principles of the accelerometer and narrowdown the design parameter space.

FIGS. 7A-7B show COMSOL simulations of a proof mass and tether system700, which includes a proof mass 710 with lateral dimensions of 2 mm×2mm and a thickness of 600 μm. Each of the four long flexures 720 a, 720b, 720 c, and 720 d (collectively referred to as flexures 720), whichfunction as tethers, is 2 mm long and 100 μm wide. In practice, thesystem 700 can be fabricated without deep Si etching and can allow theutilization of almost the entire thickness of the wafer as a proof mass.

FIG. 7A shows the simulated tether frequency as a function ofacceleration. The solid line is a linear fit to the simulated datapoints, demonstrating a scale factor of 640 Hz/g with impressivelinearity and an operating range of over 100 g. The scale factor isabout three times larger than previously demonstrated resonantaccelerometers.

FIG. 7B illustrates (not to scale) the lateral motion of the flexures720 under acceleration. The resonant frequency (ω) of the fundamentallateral mode is about 14 kHz. At this resonant frequency of the tether,the lateral displacement (x) under a high load (a) can be estimatedusing a=ω²x (x˜a/ω²). For example, under a 20,000 g load, the lateraldisplacement x is about 26 μm. Typically, this displacement does notcause significant stress issues on the large silicon flexures, but mayinduce a large strain in the silicon nitride nano-mechanical tether. Ingeneral, silicon nitride thin films can withstand axial strain levels ofup to 3% of the lateral dimension of the films without fracture. For a250 μm long tether, this displacement gives a maximum of about 7.5 μm(corresponding to about 6000 g of load).

At least two approaches can be employed to address the potential strainissues in tethers. In one example, a shock stop (e.g., see FIGS.11A-11L) can be included in the fabrication of the accelerometer with agap less than the maximum displacement of the tether (e.g., 7.5 μm inthe example above) to prevent the tether from breaking.

In another example, the length of the tethers can be decreased so as toachieve a stiffer mechanical mode, which has a higher resonant frequencyand smaller displacement under a given load. For example, doubling theresonant frequency can decrease the experienced strain down to 2.5% ofthe lateral dimension of the tether at 20,000 g, which is within thestrain limits of silicon nitride tethers. Additional parasiticmechanical modes of the tether usually occur at frequencies greater thanfour times of the frequency of the fundamental lateral mode, leading todisplacements that can be easily tolerated by both the silicon flexuresand silicon nitride tethers under a 20,000 g load.

FIGS. 8A-8B show COMSOL simulations of a proof mass and tether system800, in which the proof mass 810 has a dimension of 4 mm×4 mm and theflexures 820 a, 820 b, 820 c, and 820 d are designed to optimize themotion in the desired dimension of operation. Although the design ismore complex than the system 700 shown in FIGS. 7A-7B, the minimumfeature sizes for both devices are in fact identical, allowing the twostructures to be made in the same fabrication run.

FIG. 8A shows the simulation results, illustrating the scale factorimprovement resulting from the larger proof mass. The scale factor shownin FIG. 8A is at least ten times larger than that in currentstate-of-the-art resonating accelerometers, while still maintainingnearly linear operation over a wide acceleration range. Additionally,the added mass can reduce the noise equivalent acceleration of thedevice to below 100 ng.

Opto-Mechanical Transduction System

The opto-mechanical transduction system in a PIRA detects the vibrationfrequencies of the nanoscale tethers. The opto-mechanical transductionsystem can include an integrated optical transducer which utilizesevanescent interactions from a travelling waveguide to actuate anddetect the motion of a nearby suspended mechanical object. A siliconphotonic ring resonator can be fabricated with a small silicon nitridetether hovering at a distance slightly above the waveguide and separatedby a small air gap (e.g., <1 μm). The circuit can be excited at awavelength near one of its optical resonances (e.g., as shown in FIG.3), and small displacements in the tether can perturb the refractiveindex in the underlying optical mode such that the resonance conditionundergoes a slight shift. This shift results in a change in thetransmitted optical power which can be measured on a photodiode. Usingthis detection technique, the natural resonant frequency of themechanical tether can be identified, and any acceleration experienced bythe larger proof mass can cause the tension in the tether to change andcan be detected through the altered resonant frequency.

One factor affecting the sensitivity of a PIRA is the linewidth, orfrequency noise, of the mechanical vibration of the tether. To reducethis linewidth, an opto-mechanical oscillator (OMO) can be constructed,in which the optical dipole force of the light (also referred to asoptical pressure, radiation pressure, or light force) acting on thetether combined with the optical resonance can form a positive feedbackmechanism for mechanical motion. This can be utilized to attainself-sustained, narrow linewidth resonances in the mechanical structure,in a manner similar to quartz crystal oscillators using electronicfeedback circuitry to achieve narrow radio frequency (RF) tones.

In an OMO, when the level of direct current (DC) optical power enteringthe optical resonator exceeds a specific threshold (P_(th)), the lightcan force the tether to enter into continuous resonant motion with verylarge amplitude and very low dissipation. Stable, low dissipation (highQ factor) tether resonances can in turn increase the overallacceleration sensitivity of the device.

Factors that can affect the operation of the OMO in a PIRA include thethreshold power, at which oscillation begins (P_(th)), and the phasenoise spectrum of the oscillator, which describes the frequencystability of the tether vibration and relates to the resolution of theaccelerometer.

The threshold power of an OMO having a geometry similar to the one shownin FIG. 2A, where an optical resonator resides in close physicalproximity to a tangential nano-mechanical resonator, can be estimatedas:

$\begin{matrix}{P_{th} = {\frac{\omega_{o}^{4}}{4}\frac{m_{eff}\Omega_{m}}{Q_{o}^{3}Q_{m}g_{om}^{2}}\left( {1 + {4\frac{\Omega_{m}^{4}Q_{o}^{4}}{\omega_{o}^{4}}}} \right)}} & (2)\end{matrix}$

where ω₀ and Q_(m) are the optical and mechanical resonance frequencies,Q₀ and Q_(m) are the optical and mechanical quality factors, m_(eff) isthe effective mass of the mechanical resonator and g_(om) is theopto-mechanical coupling strength.

In one example (e.g., the OMO shown in FIG. 2A), the mechanical qualityfactor Q_(m) can be about 1×10⁶, the optical quality factor of the ringresonator Q₀ can be about 5×10⁴, and the opto-mechanical couplingstrength g_(om) can be about 1 GHz/nm. Under this condition, thethreshold optical power P_(th) is about 0.27 mW. The threshold power canbe reduced by increasing the quality factors Q₀ and Q_(m) and thecoupling strength g_(om). Optical quality factors Q₀ in the range of 10⁴and 10⁵ are readily achievable in standard silicon photonic ringresonators. Large mechanical quality factors Q_(m) can be achieved usingthe tensile strain in the silicon nitride tethers, which can providequality factors exceeding 10⁶. Strong coupling strength g_(om) can beachieved by careful design of the optical waveguide and silicon nitridetether such that interaction between the two is maximized. In oneexample, the interaction can be increased by reducing the distancebetween the ring resonator and the tether. In another example, theinteraction can be increased by increasing the interaction lengthbetween the ring resonator and the tether. For example, a racetrackshaped resonator can be used, with one of the straightaways directlyunderneath the tether. In this case, the interaction (coupling strength)between the tether and the resonator can be increased. Although a largeoptical quality factor can reduce the threshold power P_(th) to reachopto-mechanical oscillation, it may also negatively impact the phasenoise of the OMO. In practice, it can be helpful to keep the opticalquality factor at a low level as long as the threshold power is reached.

FIG. 9 shows phase noise spectra of conventional OMOs and the OMO shownin FIG. 2A by taking into account the different optical and mechanicalparameters involved in the system. The top curve in FIG. 9A shows anexample phase noise spectrum (black curve) that representsstate-of-the-art phase noise performance from an opto-mechanicaloscillator and identifies the various contributing factors into thisnoise spectrum. The phase noise of the OMO shown in FIG. 2A isrepresented by the lower curve in FIG. 9, which illustrates decreasedphase noise, especially in the lower-frequency range. The improvementsof phase noise performance in the OMO described herein can be attributedto a few particular parameters, including the reduced mechanicalresonance frequency and the increased mechanical quality factor, whichcan suppress both the thermomechanical noise of the resonator as well astechnical laser noise contributions (both phase noise and relativeintensity noise) from the input source.

Based on the phase noise performance shown in FIG. 9, the bias stabilityof the OMO can be estimated by converting the phase noise spectrum (

(ω)) to Allan variance (σ) and the frequency stability (Δf) can becalculated by:

$\begin{matrix}{{\sigma (\tau)} = {\frac{\Delta \; f}{f} = \sqrt{\int_{0}^{\infty}{\frac{4\; \omega^{2}\mathcal{L}}{\omega_{0}^{2}}\frac{\sin^{4}\left( {\omega \; {\tau/2}} \right)}{\left( \frac{\omega \; \tau}{2} \right)}\frac{\partial\omega}{\partial\pi}}}}} & (3)\end{matrix}$

The frequency stability can then be divided by the scale factor (SF=2.6kHz/g) previously calculated (see, e.g., FIGS. 6A-8B and the relevantdescriptions) to obtain bias stability.

FIGS. 10A-10B show the frequency stability Δf and the corresponding biasstability calculated using the phase noise plot in FIG. 9. Thesimulations described above illustrate that the OMO described herein iscapable of measuring accelerations down to the 100 ng level with anearly linear dynamic range greater than 100 g. This represents adynamic range of about 10⁹, which significantly exceeds the dynamicrange of the current state of the art technologies.

Accelerometer Stability/Repeatability

In the PIRAs described herein, although optical transduction is employedto achieve high sensitivity, the bias and scale factor stabilitytypically do not directly depend on the incident optical wavelength. Theoptics are used to detect the tether resonance frequency, and it is thismechanical property that primarily governs both the bias stability andscale factor of the accelerometer. The mechanical properties of theaccelerometer can in turn depend on the temperature of thenano-mechanical tether, because any change in temperature can cause achange of the Young's modulus (E) of the tether material. According toEquation (1), any change in Young's modulus can cause a shift ofvibration frequency in the tether, which can be read out as a biasdrift. Additionally, the scale factor, which can be defined as thederivative of Equation (1) with respect to acceleration a, is alsodependent on E and can undergo a shift with temperature as well. As aresult, it can be beneficial to compensate for these thermal shifts soas to maintain the bias and scale factor stability at parts per million(ppm) levels.

In one example, long-term bias drift due to temperature can becompensated for by monitoring the frequency shift of both tetherscollectively (see, e.g., FIGS. 4A-4B). Any acceleration experienced bythe proof mass in the desired dimension usually acts equally on bothtethers but with opposite force. As a result, any mutual shift in thetether frequencies can be attributed to either temperature fluctuations,or, to a much lesser degree, on proof mass displacement in an orthogonaldimension.

In another example, additional OMOs (e.g., silicon nitride OMOs) can beplaced on the chip to further reduce tether frequency shift due totemperature changes in the material. The additional OMOs can beseparated from the proof mass such that they are not affected by motionof the proof mass and only change the vibration frequency as a result oftemperature fluctuation. Each additional OMO may take less than 1 mW ofoptical power for operation, allowing multiple OMOs to be used fortemperature calibration without significantly impacting the overallpower budget. In one example, the additional OMO can be identical toFIG. 2A but without one of the tether ends fixed to a proof mass. Theaddition OMO can also be placed anywhere on the chip.

In yet another example, an insulating material can be applied to thetethers to protect the tethers from temperature changes in thesurrounding environment. The tethers can be made of highly stressedsilicon nitride, so they can sustain high packaging stresses withoutsuffering frequency shifts when insulating materials are applied.

In yet another example, an active temperature control can be employed tokeep the tether at a constant temperature. The small volume of theindividual tethers allows for their frequencies to be independentlyadjusted using nearby resistive heaters, which require very littlepower. COMSOL simulations of the PIRAs described herein suggest that itmay take only 30 mW of dropped power into one resistive heater placednear the clamping base of the tether to bring the temperature of asingle tether from −54° C. up to over 85° C. The active temperaturecontrol can be implemented in a similar manner as implemented for ovencontrolled crystal oscillators (OCXO).

In yet another example, a stable long-term reference oscillator can beincluded in the PIRA to improve bias stability. The frequency of thetether can be periodically referenced to the stable RF tone of thereference oscillator, and any drift in the tether frequency at theselong time scales can be compensated for before measurements are made.Examples of reference oscillators include temperature-compensatedcrystal oscillators (TCXOs), oven-controlled crystal oscillators(OCXOs), and chip scale atomic clocks (CSACs), among others.

Silicon Photonic Integrated Circuit

One benefit of the PIRAs described herein is that the mechanical sensingstructure seamlessly integrates with a standard silicon photonicplatform. The opto-mechanical transduction utilizes a silicon photonicring resonator which can reside on a different plane than the mechanicaltether (e.g., the ring resonator and the tether are verticallyseparated, as in FIG. 2B). This allows for the simultaneous fabricationof a multitude of other silicon photonic components alongside theopto-mechanical system. These components can be used to process theoptical signal and stabilize the optical resonator. These opticalcircuit components include grating couplers for coupling light on/offchip, phase tuners for active control of the ring resonator, andintegrated photodiodes.

The combination of integrated photodetectors and phase tuners on-chipcan be used to construct a balanced homodyne feedback circuit tomaintain stable performances of the ring resonators over temperature bypreserving a desired phase in the ring resonator such that the inputlaser wavelength always rests at the point of maximum slope (see, e.g.,FIG. 3). In this case, unwanted thermal drift can be prevented fromimpacting the optical signal-to-noise ratio. More information ofbalanced homodyne feedback circuit can be found in Cox, Jonathan A., etal.,“Control of integrated micro-resonator wavelength via balancedhomodyne locking,” Opt. Express 22.9 (2014): 11279-11289, which isincorporated herein in its entirety.

Electronic Signal Processing Circuitry

The signal processing circuity in a PIRA demodulates the accelerationsignal. In one example, rack-mounted analog RF signal processingequipment can be used to demodulate the acceleration signal. Anelectronic spectrum analyzer can be used to measure phase noise of theOMO, as well as the frequency content of specified inertial input.Frequency counters can also be used to demodulate the resonant frequencyof a particular OMO and translate any frequency shift to inertial input.Circuits of additional complexity can also be used to convert thefrequency output to a digital signal directly. In resonantaccelerometers, chip-scale demodulation techniques can leverage much ofthe infrastructure and expertise developed for RF communicationsapplications. In this example, signal processing requirements can bedetermined by digitizing the photodetector signals and utilizingcommercial signal processing simulation tools (e.g., MATLAB). Theresults from these simulations will help guide the design andconstruction for the electronic circuit. In another example, variousbonding techniques (e.g., wire-bond, flip-chip, wafer bonding, etc.) canbe employed to bond the electronic circuitry to the photonic chip.

Methods of Fabricating PIRAs Including Ring Resonators

FIGS. 11A-11L illustrate a method 1100 of fabricating PIRAs using ringresonators to measure the tether frequencies. The method 1100 beginswith a standard silicon-on-insulator (SOI) wafer including an insulatorlayer 1102 disposed on a silicon base layer 1101. A device layer 1103 isdisposed on the insulator layer 1102, as shown in FIG. 11A (crosssectional view) and FIG. 11B (top view). The device layer 1103 caninclude dielectric materials such as silicon. The thickness of thedevice layer 1103 can depend on the desired height of the resultingphotonic circuit components such as ring resonators and waveguides. Inone example, the thickness of the device layer 1103 can be about 100 nmto about 500 nm (e.g., 50 nm, 100 nm, 200 nm, 300 nm, or 500 nm).

FIGS. 11C-11D illustrate the steps of the method 1100 in which siliconphotonic integrated circuit is defined in the device layer 1103. Thedefined circuit includes a pair of ring resonators 1130 a and 1130 b(collectively referred to as ring resonators 1130), waveguides 1142 aand 1142 b that are evanescently coupled to the ring resonators 1130 aand 1130 b, respectively, and integrated photodetectors 1144 a and 1144b, optically coupled to the waveguides 1142 a and 1142 b, respectively.

FIGS. 11E-11F illustrate the fabrication of tethers. A second dielectriclayer 1104 is deposited on the ring resonators 1130, the waveguides1142, and the photodetectors 1144 for passivating the photonic circuits.A layer of stoichiometric silicon nitride can be deposited via lowpressure chemical vapor deposition (LPCVD) on the second dielectriclayer 1104. Then a pair of tethers 1120 a and 1120 b is defined from thesilicon nitride layer. This layer can be used to define the high stresssilicon nitride nano-mechanical tethers. In addition, for each tether1120 a/1120 b, a respective first anchor 1122 a/1122 b and second anchor1124 a/b are defined. The first anchor 1122 a/b can be used to fix thetether 1120 a/b on the substrate (e.g., 1104 or 1102) and the secondanchor 1124 a/b can fix the tether 1120 a/b on the proof mass to bedefined in subsequent steps.

FIGS. 11G-11H illustrate a back etching step to initiate the fabricationof a proof mass. In this step, the back side of the wafer including thesilicon base 1101 and the insulator layer 1102 can be etched down fromthe full thickness (700 μm) down to 600 μm to define the proof massregion.

FIGS. 11I-11J show the cross sectional view and the top view,respectively, of the defined proof mass 1110 suspended by the twotethers 1120 a and 1120 b to the substrate. The proof mass 1110 andassociated shock stops 1125 can be defined by, for example, a deep Sietch to penetrate entirely through the 600 μm thick Si wafer, followedby a small isotropic wet Si etch to remove any Si which remainsunderneath the tether region.

FIGS. 11K-11L illustrate the releasing of the tethers 1120 a and 1120 b.The releasing can be achieved by a controlled buffered HF wet etch toremove the dielectric materials underneath the tethers 1120 a and 1120 bso as to allow the tethers 1120 a and 1120 b to vibrate freely underforce. The etching can be followed by a critical point drying process toreduce stiction of the tethers 1120 a and 1120 b to the silicon photoniccircuit such as the ring resonators 1130 a and 1130 b. In one example,the resulting gap between the ring resonators 1130 a/b and the tethers1120 a/b can about 100 nm in vertical direction.

Alternatively, the entire proof mass 1110 can also be defined and etchedthrough the back side of the silicon base 1101. In this case, both theshock stop definition and tether release can still be accomplished onthe front side of the wafer, such as the insulating layer 1102 or thesecond dielectric layer 1104, after the proof mass 1110 is defined. Inthis case, the proof mass 1110 can encompass the full thickness of thesilicon wafer (without the initial etching as shown in FIG. 11G), whichcan be beneficial for accelerometer performance due to the added mass,but the mount for the chip may become more complex in order for theproof mass 1110 to move freely.

FIGS. 12A-12I illustrate a method 1200 of packaging a photonicintegrated resonant accelerometer so as to maintain the accelerometer ina vacuum condition (e.g., at a pressure level of about 10⁻⁵-10⁻³ Torr)and reduce or avoid squeeze-film damping in the nanosecond tethers andthe microscale proof mass. Steps in the method 1200 can be carried outduring the steps of the method 1100 illustrated in FIG. 11. Thepackaging can be carried out using wafer-scale encapsulation techniques,which can provide a sealed, high vacuum environment for MEMS devices.The batch process can also reduce packaging cost per device, improveyield, and allow for easier die singulation.

FIG. 12A shows that the method 1200 can start after the step of tetherrelease, in which tethers 1220 are defined and released from a photoniccircuit layer 1230. The photonic circuit layer 1230 can includecomponents such as ring resonators, waveguides, and photodetectors, allof which are fabricated on a wafer including a first insulator layer1202 disposed on a first silicon base 1201. FIG. 12B shows that aftertether release, a second wafer 1203 is oxide bonded to the device shownin FIG. 12A. The second wafer 1203 can include a second insulator layer1205 disposed on a second silicon base 1204. FIG. 12C shows the bondeddevice in which the photonic circuit layer 1230 and the tethers 1220 aresandwiched between two insulating layers 1202 and 1205. The secondsilicon base 1204 can be thinned on the top to fully enclose the tethers1220.

FIG. 12D shows that the bonded device is flipped over such that thefirst silicon base 1202 is upward for further processing. For example,the first silicon base 1202 can be thinned and etched to define a proofmass 1210 (not fully released as shown in FIG. 12D). FIG. 12E shows thatthe thinned first silicon base 1202 is deposited with an oxide layer1206, on which a first epitaxial layer of poly-silicon 1207 is grown.

FIG. 12F illustrates the release of the proof mass 1210 via an HF vaporprocess, after which the proof mass 1210 is suspended to the firstinsulating layer 1202 via the tethers 1220. After this, a secondepitaxial layer of poly-silicon 1208 is grown on the first epitaxiallayer of poly-silicon 1207 as shown in FIG. 12G. The second epitaxiallayer of poly-silicon 1208 can seal the fabricated components, includingthe proof mass 1210, the tethers 1220, and the photonic circuit layer1230 in a vacuum condition.

In the next step, as illustrated by FIG. 12H, the back-sealed device isflipped again such that the first silicon base 1201 is downward. Anelectronics layer 1270, including CMOS electronics 1275 and a firstoxide layer 1272, can be wafer bonded to the second silicon base 1204via, for example, oxide-oxide bonding techniques. To facilitate thebonding, a second oxide layer 1209 can be deposited on the secondsilicon base 1204 before coupling the electronics layer 1270.

FIG. 121 shows that a deep trench 1280 can be etched into the siliconportion of the electronics layer 1270 as well as the second silicon base1204. Thermo-compression solder bonding can be implemented using acommercial flip-chip bonding tool to direct light emitted from a lightsource 1290 into an entry grating coupler 1235 (part of the photoniccircuit layer 1230) designed appropriately to minimize optical lossesfrom alignment offsets. The entry grating coupler 1235 can guide thelight into the rest part of the photonic circuit layer 1230 such as ringresonators. In one example, the light source 1290 includes a surfaceemitting laser. In another example, the light source 1290 includes anedge emitting laser. The resulting device as shown in FIG. 12I includesa complete single chip accelerometer that can operate in harshconditions such as under high shock.

Alternatively, a commercial vacuum packaging service (e.g., SSTInternational) can be used to provide vacuum packaging of individualdie. Additionally, the individual chip packaging approach relies onwire-bonded electrical interfaces to the photonic circuit, which may notstand up to the extremely high shock requirements. The wafer-scaleapproach, by contrast, involves through-silicon vias and oxide bondedwafers to connect the electronic and photonic plus MEMS wafer, and canbe flip-chip bonded to a printed-circuit board.

PIRAs Using A Fabry-Perot Interferometer

Other than using ring resonators, PIRAs can also use linear resonators,which include two reflectors, to detect the tether frequencies andestimate the acceleration. One reflector in the linear resonator can befixed on a substrate while the other reflection can be attached to(e.g., disposed on or in) the tether. The motion of the proof mass cancompress or stretch the tether and change the reflectivity (and/ortransmission) of the reflector attached to the tether. Alternatively,the motion of the proof mass can change the location of the reflectorattached to the tether and change the length of the resonator. In eithercase, the resonance condition of the resonator changes accordingly,which can be manifested by the change of light beam properties (e.g.,power, spectrum, etc.) transmitted through or reflected by theresonator. As a result, monitoring the beam qualities propagatingthrough or reflected by the resonator can provide information regardingthe motion of the proof mass and according the acceleration on the proofmass.

FIGS. 13A-13B shows an accelerometer 1300 including a proof mass 1310suspended to a substrate 1360 via two tethers 1320 a and 1320 b. Thefirst tether 1320 a crosses a first linear waveguide 1330 a such thatthe first tether 1320 a is in the beam path of light beam propagating inthe first linear waveguide 1330 a. Similarly, the second tether 1320 bcrosses a second linear waveguide 1330 b and is in the beam path oflight beam propagating in the second linear waveguide 1330 b. As shownby the magnified portion in FIG. 13B, the second linear waveguide 1330 bincludes a fixed mirror 1332 b, while the second tether 1320 b includesa moving mirror 1322 b. The two mirrors 1332 b and 1322 b can form aFabry-Perot interferometer. Similarly, the first linear waveguide 1330 aand the first tether 1320 a can also include mirrors (not shown) to formanother Fabry-Perot interferometer. The accelerometer shown in FIGS.13A-13B includes only two tethers 1320 a and 1320 b, but other designsmay feature a multitude of tethers (as many as can geometrically fit ina given design) to enhance the system sensitivity or stability.

The mirrors 1332 b and 1322 b can be defined by etching a distributedBragg reflector (DBR) into the linear waveguide 1330 b and the tether1320 b, respectively. With one DBR mirror 1322 b fabricated on thetether 1320 b and free to move, and the other DBR mirror 1332 b fixedonto the silicon waveguide 1330 b, the tether motion changes theresonance condition of the cavity, which can be detected by setting thewavelength of input light to coincide with the slope of the cavity'soptical-transmission resonance and monitoring the transmitted opticalpower on a photodiode (similar to the method shown in FIG. 3). Thetether resonant frequency can then be detected by observing a peak inthe RF spectrum of the photodetector signal.

In operation, the accelerometer 1300 shown in FIGS. 13A-13B measuresacceleration along one lateral axis (one dimension). Differentdirections along that axis can be identified by looking at the directionof the tether frequency shift for each of the two tethers 1320 a and1320 b with respect to one another. Acceleration along different axescan be measured by making a second device on the same chip which isrotated by a desired amount, e.g., 90 degrees.

Optical displacement sensing can be sensitive enough to measuredisplacements due to thermal Brownian motion of small mechanicaldevices, allowing for resonant frequency detection without the need toactuate the tether motion. To improve the sensitivity of the system, theinput light can also be used to excite motion in the mechanical tethervia the photo-thermal effect, where positive feedback can lead to limitcycle oscillations in the opto-mechanical system, resulting indramatically increased mechanical quality factor (Q). In some cases, themechanical Q may be about 10⁵ or greater. The increased mechanical Q ofthe sensing tether allows for detection of smaller frequency shiftscaused by acceleration of the proof mass.

PIRAs Using Tether-Waveguide Interaction

FIGS. 14A-14B show a schematic of an accelerometer 1400 that sensesacceleration based on tether-waveguide interactions. The accelerometer1400 includes a proof mass 1410 suspended by two tethers 1420 a and 1420b to two anchors 1422 a and 1422 b, respectively, on a substrate 1460.Two waveguides 1430 a and 1430 b are disposed perpendicularly to thelongitudinal direction of the two tethers 1420 a and 1420 b,respectively, but the waveguides 1430 a and 1430 b are underneath thetethers 1420 a and 1420 b without direct physical contact. The tethers1420 a and 1420 b can be fabricated using stoichiometric silicon nitridedeposited using low pressure chemical vapor deposition (LPCVD). Thesetethers 1420 a and 1420 b can exhibit extremely high natural Q factors,which allow for high acceleration sensitivity without the need foroptically induced motion. The tethers 1420 a and 1420 b are suspended inclose proximity to the underlying waveguides 1430 a and 1430 b, in whichcase motions of the tethers 1420 a and 1420 b can perturb the evanescentfield of the waveguide mode and can be detected by either observing thedirect transmission of the light or through interferometry.

In either way, the accelerometer 1400 can be implemented in a fullyintegrated, chip-scale manner by integrating all of the optoelectroniccomponents such as lasers and photodiodes onto the same silicon photonicplatform, as depicted in FIG. 15. In another example, the detectionelectronics can also be integrated onto the same platform viawafer-level three-dimensional (3D) bonding of CMOS electronics tophotonics wafers.

FIG. 15 show a schematic of an accelerometer 1500 that includes a laser1540 coupled to a pair of photodetectors 1550 a and 1550 b via a pair ofoptical waveguides 1530 a and 1530 b, which are optically coupled torespective tethers 1520 a and 1520 b holding a proof mass 1510 from asubstrate 1501. In operation, each beam from the laser 1540 propagatesthrough a corresponding waveguide 1530 a/b to a correspondingphotodetector 1550 a/b. As the proof mass 1510 accelerates, the tethers1520 a and 1520 b move, causing light propagating through the waveguides1530 a and 1530 b to resonate in a cavity whose length changes (e.g., asin FIGS. 13A-13B), and/or to couple out of the waveguides evanescently(e.g., as in FIGS. 14A-14B). This results in changes in the amplitudesand/or phases of the beams propagating through the waveguides 1530 a and1530 b.

Phase changes can be detected interferometrically on a single detector1550 a or 1550 b. Amplitude changes can be detected using differentialdetection with a pair of photodetectors 1550 a and 1550 b as in FIG. 15.Differential detection allows for cancellation of unwanted long-termdrift. In addition, differential detection can be performed withdifferent sources, e.g., one source per waveguide. However, performingdifferential detection using light from the same source 1540 in multiplewaveguides 1530 a and 1530 b can help cancel some noise in the sourceitself (e.g., relative intensity noise). The signals acquired by thedetectors 1550 a and 1550 b are transmitted to two frequency detectors1560 a and 1560 b, operably coupled to a frequency reference 1570 (e.g.,a voltage-controlled oscillator), to estimate the frequency the tethers1520 a and 1520 b. Based on the estimated tether frequencies, aprocessing unit 1580 can then calculate the acceleration originallyimposed on the proof mass 1510.

Photonic integrated resonant accelerometers may allow for improvementsin many device parameters over current MEMS devices includingsensitivity, scale factor stability, bias stability, dynamic range, andbandwidth. Many of these limitations stem from the electro-statictransduction technique used by conventional devices. The optical systemdisclosed herein overcomes these limitations while still providing achip-scale system which can be batch fabricated and maintain low size,weight, power, and cost. The potential applications for this technologyhave a broad range from industrial sensors to inertial navigation, orany application where the robustness and sensitivity of currentaccelerometers needs to be improved.

Methods of Fabricating PIRAs Using Linear Resonators and Waveguides

FIGS. 16A-16F shows a fabrication flow of accelerometers using linearresonators (e.g., shown in FIGS. 13A-13B) or tether-waveguideinteractions (e.g., shown in FIGS. 14A-14B). In FIG. 16A, a standardsilicon-on-insulator (SOI) wafer including a silicon base 1601, an oxidelayer 1602, and a device layer 1603 (e.g., silicon), is provided. InFIG. 16B, photonic waveguides 1630 are defined by, for example,partially etching the device layer 1603 similarly to standard siliconphotonic techniques. A second oxide layer 1604 is then deposited on thefabricated waveguides 1630, as shown in FIG. 16C.

In FIG. 16D, a sensing tether 1620 is defined by, for example, etchingfully through the second oxide layer 1604 and the buried oxide layer1602 in the wafer until reaching the silicon base 1601. A proof mass1610 can then be defined by etching fully through the thickness of thesilicon base 1601 from the back side using a deep reactive ion etch(DRIE), as shown in FIG. 16E. DRIE is a common tool used in MEMSfabrication techniques. Finally, as shown in FIG. 16F, the sensingtether can be released by using a timed hydrofluoric acid (HF) etch toremove a small amount of silicon dioxide underneath the sensing tether.Since the tether may have cross-sectional dimensions on the order of 1μm, this etch may remove as little as about 500 nm of oxide from eitherside of the tether, leaving little lasting damage to the remainder ofthe oxide on the wafer. If desired, molybdenum can be used protect oxidefrom the HF etch, as the etch rate is much slower on molybdenum than onthe oxide itself.

CONCLUSION

While various inventive embodiments have been described and illustratedherein, those of ordinary skill in the art will readily envision avariety of other means and/or structures for performing the functionand/or obtaining the results and/or one or more of the advantagesdescribed herein, and each of such variations and/or modifications isdeemed to be within the scope of the inventive embodiments describedherein. More generally, those skilled in the art will readily appreciatethat all parameters, dimensions, materials, and configurations describedherein are meant to be exemplary and that the actual parameters,dimensions, materials, and/or configurations will depend upon thespecific application or applications for which the inventive teachingsis/are used. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific inventive embodiments described herein. It is,therefore, to be understood that the foregoing embodiments are presentedby way of example only and that, within the scope of the appended claimsand equivalents thereto, inventive embodiments may be practicedotherwise than as specifically described and claimed. Inventiveembodiments of the present disclosure are directed to each individualfeature, system, article, material, kit, and/or method described herein.In addition, any combination of two or more such features, systems,articles, materials, kits, and/or methods, if such features, systems,articles, materials, kits, and/or methods are not mutually inconsistent,is included within the inventive scope of the present disclosure.

Also, various inventive concepts may be embodied as one or more methods,of which an example has been provided. The acts performed as part of themethod may be ordered in any suitable way. Accordingly, embodiments maybe constructed in which acts are performed in an order different thanillustrated, which may include performing some acts simultaneously, eventhough shown as sequential acts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, “or” should beunderstood to have the same meaning as “and/or” as defined above. Forexample, when separating items in a list, “or” or “and/or” shall beinterpreted as being inclusive, i.e., the inclusion of at least one, butalso including more than one, of a number or list of elements, and,optionally, additional unlisted items. Only terms clearly indicated tothe contrary, such as “only one of” or “exactly one of,” or, when usedin the claims, “consisting of,” will refer to the inclusion of exactlyone element of a number or list of elements. In general, the term “or”as used herein shall only be interpreted as indicating exclusivealternatives (i.e. “one or the other but not both”) when preceded byterms of exclusivity, such as “either,” “one of,” “only one of,” or“exactly one of” “Consisting essentially of,” when used in the claims,shall have its ordinary meaning as used in the field of patent law.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively, as set forth in the United States Patent Office Manual ofPatent Examining Procedures, Section 2111.03.

1. An accelerometer comprising: a proof mass; a first tether,mechanically coupled to a first side of the proof mass, to vibrate inresponse to acceleration of the proof mass; a first ring resonatorevanescently coupled to the first tether, wherein vibration of the firsttether causes a change of a first resonance condition of the first ringresonator; a detection system, operably coupled to the first ringresonator, to sense the change of the first resonance condition of thefirst ring resonator.
 2. The accelerometer of claim 1, wherein the firsttether comprises at least one of silicon or silicon nitride.
 3. Theaccelerometer of claim 1, wherein the first tether has a widthsubstantially equal to or less than 1 μm.
 4. The accelerometer of claim1, wherein the first tether has an internal tensile stress substantiallyequal to or greater than 500 MPa.
 5. The accelerometer of claim 1,wherein the first vibration of the first tether has a vibrationfrequency of about 50 KHz to about 1 GHz.
 6. The accelerometer of claim1, wherein a distance between the first ring resonator and the firsttether is about 100 nm to about 300 nm.
 7. The accelerometer of claim 1,wherein the detection system comprises: a waveguide, evanescentlycoupled to the first ring resonator, to guide light past the first ringresonator so as to couple a portion of the light into the first ringresonator; and a detector, optically coupled to the waveguide, to detecta change in the portion of the light coupled into the first ringresonator caused by the change of the first resonance condition of thefirst ring resonator.
 8. The accelerometer of claim 7, furthercomprising: a substrate to support the first ring resonator and thedetector; and a semiconductor laser, fabricated in the substrate andoptically coupled to the first ring resonator, to provide the lightbeam.
 9. The accelerometer of claim 7, wherein the light beam has apower greater than 0.2 mW so as to cause an opto-mechanical oscillationof the first tether.
 10. The accelerometer of claim 1, furthercomprising: a second tether mechanically coupled to a second side,opposite the first side, of the proof mass, to vibrate in response tothe acceleration of the proof mass; and a second ring resonator,evanescently coupled to the second tether, wherein vibration of thesecond tether causes a change of a second resonance condition of thesecond ring resonator, wherein the detection system senses the change ofthe second resonance condition of the second ring resonator.
 11. Theaccelerometer of claim 1, further comprising: an opto-mechanicaloscillator, operably coupled to the detection system, to monitor atemperature fluctuation of the accelerometer.
 12. The accelerometer ofclaim 1, further comprising: a heater, thermally coupled to the firsttether, to keep the first tether at a constant temperature so as tomitigate thermal drift.
 13. A method of sensing acceleration with anaccelerometer comprising a proof mass, a first tether mechanicallycoupled to a first side of the proof mass, and a first ring resonatorevanescently coupled to the first tether, the method comprising:detecting a change of a first resonance condition of the first ringresonator caused by vibration of the first tether; and estimating theacceleration based at least in part on the change of the first resonancecondition of the first tether in response to acceleration of the proofmass.
 14. The method of claim 13, wherein detecting the change of thefirst resonance condition of the first ring resonator comprises:detecting a change in an amount of light evanescently coupled into thefirst ring resonator.
 15. The method of claim 14, wherein transmittingthe light beam comprises transmitting the light beam having a powergreater than 0.2 mW so as to cause opto-mechanical oscillation of thefirst tether in the accelerometer.
 16. The method of claim 13, whereinthe accelerometer further comprises a second tether mechanically coupledto a second side, opposite the first side, of the proof mass, a secondring resonator evanescently coupled to the second tether, the methodfurther comprising: detecting a change of a second resonance conditionof the second ring resonator caused by vibration of the second tether inresponse to the acceleration of the proof mass; and estimating theacceleration based at least in part on the change of the first resonancecondition of the first ring resonator and the change of the secondresonance condition of the second ring resonator.
 17. The method ofclaim 13, further comprising: monitoring a temperature fluctuation ofthe accelerometer using an opto-mechanical oscillator so as to mitigatethermal noise in sensing the acceleration.
 18. The method of claim 13,further comprising: maintaining the first tether at a constanttemperature so as to mitigate thermal noise in sensing the acceleration.19. A method of fabricating an accelerometer, the method comprising:fabricating a first ring resonator in a first dielectric layer disposedon a substrate; depositing a second dielectric layer on the first ringresonator; fabricating a first tether on the second dielectric layer;defining a proof mass mechanically coupled to the first tether byetching a back surface of the substrate; and etching the seconddielectric layer below the first tether so as to release the firsttether from the first ring resonator.
 20. The method of claim 19,wherein fabricating the first ring resonator comprises: depositing anepitaxial layer on the substrate; and etching the epitaxial layer so asto define the first ring resonator.
 21. The method of claim 20, furthercomprising: etching the epitaxial layer so as to define a waveguideoptically coupled to the first ring resonator; and forming a detector,optically coupled to the waveguide, on the substrate.
 22. The method ofclaim 19, wherein fabricating the first tether comprises: depositing alayer of stoichiometric silicon nitride on the second dielectric layervia low pressure chemical vapor deposition; and etching the layer ofstoichiometric silicon nitride so as to define the first tether.
 23. Themethod of claim 19, wherein releasing the first tether comprises:etching the second dielectric layer using buffered HF etching; and pointdrying the first tether so as to reduce stiction between the firsttether and the first ring resonator.
 24. The method of claim 19, furthercomprising: disposing another substrate on the first tether so as toenclose the first tether in vacuum.
 25. The method of claim 19, furthercomprising: growing an epitaxial layer on the back surface of thesubstrate to encapsulate the proof mass in vacuum.
 26. The method ofclaim 19, further comprising: fabricating a light source on thesubstrate to provide a light beam propagating in the first ringresonator.
 27. An accelerometer comprising: a semiconductor substrate; aproof mass, suspended from the semiconductor substrate by a first tetherand a second tether, to move in a first direction in response to a forceapplied to the accelerometer; a first optical waveguide, opticallycoupled to the first tether, to guide a first optical beam in a seconddirection orthogonal to the first direction such that motion of theproof mass causes a change in optical coupling between the first opticalwaveguide and the first tether; a second optical waveguide, opticallycoupled to the second tether, to guide a second optical beam in thesecond direction such that the motion of the proof mass causes a changein optical coupling between the second optical waveguide and the secondtether; a first photodetector, in optical communication with the firstoptical waveguide, to sense a change in frequency and/or amplitude ofthe first optical beam caused by the change in optical coupling betweenthe first optical waveguide and the first tether; and a secondphotodetector, in optical communication with the second opticalwaveguide, to sense a change in frequency and/or amplitude of the secondoptical beam caused by the change in optical coupling between the secondoptical waveguide and the second tether.
 28. The accelerometer of claim27, wherein the first optical waveguide is evanescently coupled to thefirst tether.
 29. The accelerometer of claim 27, further comprising: afirst reflector disposed on the first tether in optical communicationwith the first optical waveguide; and a second reflector disposed in thefirst optical waveguide so as to form an optical cavity having a lengththat changes in response to the force applied to the accelerometer. 30.The accelerometer of claim 27, further comprising: differentialdetection circuitry, in electrical communication with the firstphotodetector and the second photodetector, to generate a differencesignal based on the change in frequency and/or amplitude of the firstoptical beam and the change in frequency and/or amplitude of the secondoptical beam, the difference signal representing the force applied tothe accelerometer.